(CNN) -- Saudi Arabia could have helped the United States prevent al Qaeda's 2001 attacks on New York and Washington if American officials had consulted Saudi authorities in a "credible" way, the kingdom's former ambassador said in a documentary aired Thursday.

The comments by Prince Bandar bin Sultan are similar to the remarks this week by Saudi King Abdullah that suggested Britain could have prevented the July 2005 train bombings in London if it had heeded warnings from Riyadh.

Speaking to the Arabic satellite network Al-Arabiya on Thursday, Bandar -- now Abdullah's national security adviser -- said Saudi intelligence was "actively following" most of the September 11, 2001, plotters "with precision."

"If U.S. security authorities had engaged their Saudi counterparts in a serious and credible manner, in my opinion, we would have avoided what happened," he said. Watch Bandar's comments »

Bandar was the Saudi ambassador to Washington for nearly 22 years before he was replaced in 2005. A knowledgeable U.S. official told CNN that Bandar's comments should be taken "with a grain of salt."

On Monday, Abdullah told the BBC that Saudi Arabia had sent warnings to British authorities before the London subway bombings that killed 52 people -- the city's bloodiest day since World War II.

"We have sent information to Great Britain before the terrorist attacks in Britain," Abdullah said. "But unfortunately, no action was taken, and it may have been able to avert the tragedy."

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The September 11 attacks killed nearly 3,000 people in New York, Washington and Pennsylvania. All but four of the suicide hijackers who carried out the plot were Saudi nationals, and after the attacks, the kingdom was widely criticized for having tolerated Islamic militancy.

The Saudis have called the criticism unfair, pointing out that al Qaeda founder Osama bin Laden's original grievance was against the country's ruling family, which invited U.S. troops into the kingdom after the Iraqi invasion of Kuwait in 1990.

A string of attacks on Western compounds, oil installations and Saudi institutions between 2003 and 2006 were blamed on al Qaeda's followers.

And Saudi officials say that since 9/11, they have taken steps to ensure charitable donations do not fall into the hands of al Qaeda.E-mail to a friend